FLASH-MAX embeds exact Maxwell solutions as neurons in a neural network to reconstruct homogeneous EM fields from sparse data with guaranteed zero PDE residual and proven universal approximation on arbitrary domains.
Physics-informed neural operator for learning partial differential equations.ACM/IMS Journal of Data Science, 1(3):1–27
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Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
CLDNet is a conditional latent dynamics network surrogate for the shallow water equations that delivers 115x faster 96-hour flood forecasts on irregular metropolitan basins while maintaining usable accuracy against gauge data.
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
The review summarizes progress toward faster, automated imaging-derived FFR using ML/DL and physics-informed approaches like PINNs and PINOs, while noting challenges in generalizability and the need for clinical validation.
citing papers explorer
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Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
FLASH-MAX embeds exact Maxwell solutions as neurons in a neural network to reconstruct homogeneous EM fields from sparse data with guaranteed zero PDE residual and proven universal approximation on arbitrary domains.
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Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
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Solving Convolution-type Integral Equations using Preconditioned Neural Operators
A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
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Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations
CLDNet is a conditional latent dynamics network surrogate for the shallow water equations that delivers 115x faster 96-hour flood forecasts on irregular metropolitan basins while maintaining usable accuracy against gauge data.
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A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
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Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
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Imaging-Derived Coronary Fractional Flow Reserve: Advances in Physics-Based, Machine Learning, and Physics-Informed Methods
The review summarizes progress toward faster, automated imaging-derived FFR using ML/DL and physics-informed approaches like PINNs and PINOs, while noting challenges in generalizability and the need for clinical validation.